Two-dimensional shock–bubble interaction is an analogy of the steady three-dimensional jet flow in a scramjet. On the basis of Navier–Stokes simulations, a cylindrical bubble embedded with hydrogen surrounded by air was accelerated by a shock. The evolution can be divided into the lobe-emergence stage, the back-lobe suction stage, and the equilibrium stage. Based on the inhomogeneity between the hydrogen mass fraction and the vorticity field, a correlation coefficient is proposed to quantitatively determine the starting moment of the equilibrium stage. In the equilibrium stage, quasi-Gaussian distributions are modeled for the mass fraction and the vorticity. Surface integrals are performed to derive corresponding mixedness and circulation models, both controlled by two statistical parameters (standard deviation and peak value). Such Gaussian integrated models are universal for different cylindrical bubble aspect ratios ( $$\mathrm {AR}=0.5$$ AR = 0.5 –2) and shock Mach numbers ( $$M=1.22$$ M = 1.22 –2). They provide a statistical perspective of late-time SBI evolution in addition to the description from certain physical quantities and help better understand the compressible mixing of scramjet combustors.

中文翻译：

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二维冲击-轻型圆柱气泡相互作用后期演化的高斯模型

二维激波-气泡相互作用类似于超燃冲压发动机中稳定的三维射流。在 Navier-Stokes 模拟的基础上，一个被空气包围的嵌入氢气的圆柱形气泡通过冲击加速。演化可分为叶出现阶段、叶后吸入阶段和平衡阶段。基于氢质量分数与涡量场之间的不均匀性，提出了相关系数来定量确定平衡阶段的起始时刻。在平衡阶段，模拟高斯分布的质量分数和涡度。执行表面积分以导出相应的混合度和循环模型，两者均由两个统计参数（标准偏差和峰值）控制。这种高斯积分模型对于不同的圆柱气泡纵横比（$$\mathrm {AR}=0.5$$ AR = 0.5-2）和冲击马赫数（$$M=1.22$$M = 1.22-2）是通用的。除了某些物理量的描述外，它们还提供了后期 SBI 演变的统计视角，并有助于更好地了解超燃冲压发动机燃烧器的可压缩混合。